Individuals with low memory capacity perform poorly on fluid intelligence and attentional control tasks. Here, we examined whether low working memory performance is due to a reduced capacity, or if it is instead due to more frequent states of general inattention during the task. We used a whole report visual memory procedure and defined attentional lapses as trials in which individuals reported only one or fewer items correctly. Lower capacity individuals, as measured with a change detection task, had an average of 12.1% lapse trials, while high capacity individuals had 7.4% lapses. Thus, while low capacity individuals had more frequent states of inattentiveness, this factor did not account for all of the differences between them and their high capacity counterparts. Further, while all subjects lapsed more frequently for supra capacity arrays, low capacity individuals showed a much greater increase in inattentiveness during these trials. In a followup experiment, we examined whether this increase in lapses for large arrays was due to the high memory load or if it was due to an increased demand for attentional control. In one condition, subjects were shown arrays of 6 items and were precued to remember only a subset of the items, which allowed us to separately manipulate the memory load from the need to exert attentional control within the trial. Lapse frequency was high when subjects needed to exert attentional control irrespective of the number of items to be remembered, suggesting that the increase in lapses for large arrays was due attentional control demands rather than the memory load. Together, these results reveal that some, but not all, of the differences in performance between high and low capacity individuals are determined by the frequency of lapse trials, and this contribution is magnified under circumstances that require attentional control.